If ` 31 x + 31 y = 4 0 3` , then what is the average of x and y ?

Options

A. `3 . 5 `
B. 5
C. `6 . 5`
D. 13

Answer

To solve the equation \( 31x + 31y = 403 \) and find the average of \( x \) and \( y \), we can follow these steps:

### Step 1: Simplify the equation
We can factor out the common term from the left side of the equation:
\[ 31(x + y) = 403 \]

### Step 2: Isolate \( x + y \)
To isolate \( x + y \), we divide both sides of the equation by 31:
\[ x + y = \frac{403}{31} \]

### Step 3: Calculate \( \frac{403}{31} \)
Now we perform the division:
\[ \frac{403}{31} = 13 \]
So, we have:
\[ x + y = 13 \]

### Step 4: Find the average of \( x \) and \( y \)
The average of two numbers \( x \) and \( y \) is given by the formula:
\[ \text{Average} = \frac{x + y}{2} \]
Substituting the value of \( x + y \):
\[ \text{Average} = \frac{13}{2} = 6.5 \]

### Final Answer
Thus, the average of \( x \) and \( y \) is \( 6.5 \).

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